結果

問題 No.1497 Triangle
ユーザー square1001
提出日時 2021-05-03 22:52:33
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 3,886 bytes
コンパイル時間 1,305 ms
コンパイル使用メモリ 96,292 KB
実行使用メモリ 9,088 KB
最終ジャッジ日時 2024-07-22 13:06:03
合計ジャッジ時間 7,424 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3 WA * 1
other AC * 16 WA * 2 TLE * 1 -- * 28
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int gcd(int x, int y) {
    if(y == 0) return x;
    return gcd(y, x % y);
}
int main() {
    int N;
    cin >> N;
    vector<int> X(N), Y(N);
    for(int i = 0; i < N; ++i) {
        cin >> X[i] >> Y[i];
    }
    vector<vector<int> > lines; // {a, b, c} --> ax + by + c = 0
    for(int i = 0; i < N; ++i) {
        for(int j = 0; j < i; ++j) {
            int a = Y[i] - Y[j];
            int b = -(X[i] - X[j]);
            int c = -(a * X[i] + b * Y[i]);
            int g = gcd(abs(a), gcd(abs(b), abs(c)));
            if(a < 0 || (a == 0 && b < 0)) {
                a *= -1, b *= -1, c *= -1;
            }
            lines.push_back({a / g, b / g, c / g});
        }
    }
    sort(lines.begin(), lines.end());
    lines.erase(unique(lines.begin(), lines.end()), lines.end());
    int ls = lines.size();
    vector<bool> ok(1 << N, false);
    ok[0] = true;
    for(int i = 0; i < N; ++i) {
        ok[1 << i] = true;
    }
    vector<vector<int> > online(ls), orth(ls);
    for(int i = 0; i < ls; ++i) {
        for(int j = 0; j < N; ++j) {
            if(lines[i][0] * X[j] + lines[i][1] * Y[j] + lines[i][2] == 0) {
                online[i].push_back(j);
                orth[i].push_back(lines[i][1] * X[j] - lines[i][0] * Y[j]);
            }
        }
        sort(online[i].begin(), online[i].end(), [&](int va, int vb) {
            return lines[i][1] * (X[vb] - X[va]) - lines[i][0] * (Y[vb] - Y[va]) > 0;
        });
        sort(orth[i].begin(), orth[i].end());
    }
    for(int i = 0; i < ls; ++i) {
        int sz = online[i].size();
        for(int j = 0; j <= sz; ++j) {
            for(int k = j + 1; k <= sz; ++k) {
                int bit = 0;
                for(int l = j; l < k; ++l) {
                    bit |= 1 << online[i][l];
                }
                ok[bit] = true;
            }
        }
    }
    /*
    for(int i = 0; i < ls; ++i) {
        cout << lines[i][0] << ' ' << lines[i][1] << ' ' << lines[i][2] << endl;
    }
    */
    for(int i = 0; i < ls; ++i) {
        for(int j = 0; j < i; ++j) {
            for(int k = 0; k < j; ++k) {
                if(lines[i][0] * lines[j][1] == lines[i][1] * lines[j][0]) continue;
                if(lines[j][0] * lines[k][1] == lines[j][1] * lines[k][0]) continue;
                if(lines[k][0] * lines[i][1] == lines[k][1] * lines[i][0]) continue;
                vector<int> pos = { i, j, k };
                vector<int> sign(3);
                bool nonzero = true;
                for(int w = 0; w < 3; ++w) {
                    int p0 = pos[w], p1 = pos[(w + 1) % 3], p2 = pos[(w + 2) % 3];
                    long long val0 = lines[p0][2] * (lines[p2][0] * lines[p1][1] - lines[p1][0] * lines[p2][1]);
                    long long val1 = lines[p1][2] * (lines[p0][0] * lines[p2][1] - lines[p2][0] * lines[p0][1]);
                    long long val2 = lines[p2][2] * (lines[p0][0] * lines[p1][1] - lines[p1][0] * lines[p0][1]);
                    long long val = (val0 + val1 - val2) * (lines[p2][0] * lines[p1][1] - lines[p1][0] * lines[p2][1] > 0 ? +1 : -1);
                    if(val == 0) {
                        nonzero = false;
                        break;
                    }
                    sign[w] = (val > 0 ? +1 : -1);
                }
                if(!nonzero) continue;
                for(int w1 : orth[i]) {
                    for(int w2 : orth[j]) {
                        for(int w3 : orth[k]) {
                            for(int b = 0; b < 8; ++b) {
                                int bit = 0;
                                for(int l = 0; l < N; ++l) {
                                    int vali = lines[i][0] * X[l] + lines[i][1] * Y[l] + lines[i][2];
                                    int valj = lines[j][0] * X[l] + lines[j][1] * Y[l] + lines[j][2];
                                    int valk = lines[k][0] * X[l] + lines[k][1] * Y[l] + lines[k][2];
                                    if(vali == 0) vali += (lines[i][1] * X[l] - lines[i][0] * Y[l] >= w1 ? +1 : -1) * ((b & 1) ? +1 : -1);
                                    if(valj == 0) valj += (lines[j][1] * X[l] - lines[j][0] * Y[l] >= w2 ? +1 : -1) * ((b & 2) ? +1 : -1);
                                    if(valk == 0) valk += (lines[k][1] * X[l] - lines[k][0] * Y[l] >= w3 ? +1 : -1) * ((b & 4) ? +1 : -1);
                                    if(vali * sign[0] >= 0 && valj * sign[1] >= 0 && valk * sign[2] >= 0) {
                                        bit |= 1 << l;
                                    }
                                }
                                ok[bit] = true;
                            }
                        }
                    }
                }
            }
        }
    }
    int res = 0;
    for(int i = 0; i < (1 << N); ++i) {
        if(ok[i]) {
            /*
            for(int j = 0; j < N; ++j) {
                cout << ((i >> j) & 1);
            }
            cout << endl;
            */
            ++res;
        }
    }
    cout << res << endl;
    return 0;
}
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